Parallel data counter circuit
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 US5619437A US5619437A US08534714 US53471495A US5619437A US 5619437 A US5619437 A US 5619437A US 08534714 US08534714 US 08534714 US 53471495 A US53471495 A US 53471495A US 5619437 A US5619437 A US 5619437A
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 G—PHYSICS
 G06—COMPUTING; CALCULATING; COUNTING
 G06F—ELECTRICAL DIGITAL DATA PROCESSING
 G06F7/00—Methods or arrangements for processing data by operating upon the order or content of the data handled
 G06F7/60—Methods or arrangements for performing computations using a digital nondenominational number representation, i.e. number representation without radix; Computing devices using combinations of denominational and nondenominational quantity representations, e.g. using difunction pulse trains, STEELE computers, phase computers
 G06F7/607—Methods or arrangements for performing computations using a digital nondenominational number representation, i.e. number representation without radix; Computing devices using combinations of denominational and nondenominational quantity representations, e.g. using difunction pulse trains, STEELE computers, phase computers numberofones counters, i.e. devices for counting the number of input lines set to ONE among a plurality of input lines, also called bit counters or parallel counters
Abstract
Description
1. Field of the Invention
The present invention relates to parallel data counter circuits, and more specifically, to parallel data counter circuits which calculate the total numbers of "1"'s or "0"'s in parallel data which is generated in synchronization with a clock.
2. Description of the Related Art
Hereinbelow, an example of a conventional parallel data counter circuit will be explained with reference to FIG. 6. FIG. 6 shows a parallel data counter circuit which calculates the number of "1"'s in four parallel groups of data comprising four mbit counter circuits 69. The mbit counter circuits 69 respectively have parallel data input terminals 2023, and each of their input sides are connected to a clock terminal 30, a storage signal input terminal 40, and a reset terminal 50. Initially, storage data output terminals 7073 are respectively connected to the output sides of mbit counter circuits 69.
As examples of mbit counter circuits 69, it is possible to use those comprising an mbit counter 200 and a storage circuit 201 such as that shown in FIG. 7. A data input terminal 220, a clock input terminal 230 and a reset terminal 250 are connected to mbit counter 200, while a storage signal input terminal 240 and a storage data output terminal 270 are connected to the storage circuit
In the mbit counter circuit of FIG. 7, mbit counter 200 performs a count by means of clock signal 230A input from clock terminal 230, with data 220A input from data input terminal 220 as a control signal. In this example, mbit counter 200 has a control structure such that the clock signal 230A counts up when the data 220A is equal to 1. The count value 200A of this mbit counter 200 is inputted to the storage circuit 201.
In order to read out the count value for a given time, storage circuit 201 stores the count Value 200A according to a signal 240A input to the storage signal terminal 240. Then the count value 200A is output from storage data output terminal 270 as an output signal 270A. The mbit Counter 200 is initialized when a reset signal 250A is input to reset terminal 250.
Next, the operation of a conventional parallel data counter circuit will be explained with reference to FIG. 6. Four pieces of parallel data 20A23A which have been input to data input terminals 2023, are respectively input to the data input terminals of mbit counter circuits 69. The mbit counter circuits 69 perform calculations based on clock signal 30A input from clock input terminal 30.
When reading out the results of the calculations in the parallel data counter circuit at a given time, a signal 40A in synchronization with clock signal 30A is input to storage signal input terminal 40. The signal 40A is input to the storage signal input terminals of the mbit counter circuit 69. Then, each of the mbit counter circuits 69 stores the calculated value for that time and outputs storage data 6A9A. These storage data 6A9A are output from the storage data output terminals 7073. When a reset signal 50A is input to reset terminal 50, each mbit counter circuit 69 is initialized, thereby initializing the parallel data counter circuit of FIG. 6.
Next, the procedure for calculating all of the calculation values in the parallel data counter circuit from the abovementioned storage data will be explained. The storage data 6A9A for a given time are equal to the calculation values of the four parallel data 20A23A respectively. Therefore, the total calculation value of the parallel data counter circuit is 6A+7A+8A+9A.
While FIG. 6 shows an example of a quadruple parallel data counter circuit, it is possible to have an nparallel data counter circuit provided with n mbit counter circuits for n groups of data. Additionally, the total calculated value for such as case, when taking the calculated value for each mbit counter circuit to be X_{n}, would be ΣX_{n}.
However, with conventional parallel data counter circuits, it is necessary to provide n counter circuits corresponding to n parallel data in order to calculate the total value over all of the data. For this reason, the number of counter circuits increases with the number of parallel data to be calculated, which can lead to problems with enlargement of the circuit.
Additionally, it is necessary to, increase the number of bits m for each counter circuit when increasing the count number of the counter circuit. When the bit number m of each counter circuit is increased in this way, there is a problem in that the size of the circuit could increase even further by m times for the n parallel data over the entire parallel data counter circuit.
The object of the present invention is to provide a parallel data counter circuit which is able to handle increases in the amount of parallel data or the count number with only a small increase in the size of the circuit.
In order to realize the above object, the present invention offers a parallel data counter circuit which calculates the total number of "1"'s or "0"'s in a set of parallel data, comprising k addition means, wherein k is an integer greater than 2; and wherein first addition means add said parallel data two pieces at a time and output carry signals corresponding to the additions; nth addition means, wherein n represents every integer between 1 and k, add the carry signals output from the (n 1)th addition means two at ma time and output carry signals corresponding to the additions; kth addition means add the carry signals output from the (k1)th addition means two at a time and output carry signals corresponding to the additions; and counter means which calculates carry signals output from the kth addition means.
Additionally, with the present invention, it is not necessary to provide parallel counter circuits corresponding to the parallel data number as in, the conventional examples, thereby preventing increases in the size of the circuit in response to the number of parallel data.
Furthermore, by providing a parallel data counter circuit with a single counter means which does not depend on the parallel data number, it is possible to handle the increase or decrease of the maximum count number with an increase or decrease of the bit number of the single counter means.
FIG. 1 is a circuit diagram illustrating an embodiment of the parallel data counter circuit according to the present invention.
FIG. 2 is a circuit diagram illustrating an example of an addition circuit used in the embodiment shown in FIG. 1.
FIG. 3 is a time chart for explaining the operation of the embodiment shown in FIG. 1.
FIG. 4 is a circuit diagram illustrating another embodiment of a parallel data counter circuit or,the present invention.
FIG. 5 is a circuit diagram illustrating an example of an addition circuit used in the embodiment shown in FIG. 4.
FIG. 6 is a circuit diagram illustrating a conventional parallel data counter circuit.
FIG. 7 is a circuit diagram illustrating an example of the composition of a counter circuit used in the conventional example shown in FIG. 6.
Next, an example of an embodiment of the parallel data counter circuit will be explained with reference to FIG. 1. FIG. 1 shows a first addition means comprising addition circuits 1 and 2, a second addition means comprising addition circuit 3, and a counter means comprising an mbit counter circuit 4. Additionally in FIG. 1, reference numerals 2023 indicate parallel data terminals, reference numeral 30 indicates a clock terminal, reference numerals 4042 indicate storage signal terminals, reference numeral 50 indicates a reset terminal and reference numerals 6062 indicate storage data output terminals.
FIG. 1 illustrates an example of a quadruple parallel data counter circuit for calculating the number of "1"'s in quadruple parallel data, having a parallel number which is a power of two. Since mbit counter circuit 4 of the present embodiment has the same composition as that of the conventional example, a detailed explanation will be omitted.
Next, an example of the composition of addition circuits 13 which are the basic component circuits of the embodiment shown in FIG. 1 will be explained with reference to FIG. 2. As shown in FIG. 2, the addition circuit comprises a full adder 100 which is an adding device, DFFs 101/102 having reset function and storage circuit 103. Additionally, reference numerals 120 and 121 indicate data input terminals, reference numeral 130 indicates a clock terminal, reference numeral 140 indicates a storage signal terminal, reference numeral 150 indicates a reset terminal, reference numeral 170 indicates a carry output terminal and reference numeral 160 indicates a storage data output terminal.
Two pieces of parallel data 120A and 121A, after being entered into data input terminals 120 and 121, are input to full adder 100 along with the addition result 102A from the previous step. The full adder 100 adds the parallel data 120A and 121A with the addition result 102A. Then, if the addition result is greater than or equal to 2, a carry signal 100A which is a signal to jump up one place is output. This carry signal 100A is input to DFF 101. The DFF 101 times the carry signal 100A with a clock signal 130A input from the clock terminal 130, and outputs carry data 101A. This carry data 101A is output from carry output terminal 170.
Additionally, full adder 100 outputs addition result 100B if the addition results in a 1 or a 3. The addition result 100B is retimed with the clock signal 130A by DFF 102. The addition result 102A retimed by DFF 102 is input to full adder 100 in order to add it with the next parallel data 120A and 121A as the addition results of the previous step.
Also, the addition result 102A is input to storage circuit 103. The storage circuit 103 stores the current addition result 102A and outputs an addition signal 103A according to a signal 140A input to storage signal terminal 140 to read out the calculation result for a given time. The addition signal 103A is output from output terminal 160. The DFF 101 and DFF 102 are initialized by inputting a reset signal 150A to reset terminal 150.
Next, the actions of the embodiment of a quadruple parallel data counter circuit shown in FIG. 1 will be explained. Of the four pieces of parallel data 20A23A input to the data input terminals 2023, parallel data 20A and 21A are input to addition circuit 1, while parallel data 22A and 23A are input to addition circuit 2. Then, the parallel data 20A and 21A are added at addition circuit 1 comprising the first addition means. If a carry is generated upon performing the addition, addition circuit 1 generates a carry signal 1A which has been retimed with the clock signal 30A input to clock terminal 30. In a similar manner, at addition circuit 2, the parallel data 22A and 23A are added, and if a carry is generated, then a carry signal 2A is generated.
The carry signals 1A and 2A of addition circuits 1 and 2 are input to addition circuit 3 of the second addition means. At addition circuit 3, the carry signals 1A and 2A are input and added; if a carry is generated, then a carry signal 3A which has been retimed with the clock signal 30A is generated. The carry signal 3A is input to the counter circuit 4. The counter circuit 4 counts the clock signal 30A depending on the state of the carry signal 1A.
With this parallel data counter circuit, when a calculation result is read out for a given time, a storage signal 40A in synchronization with the clock signal 30A is first input from storage signal terminal 40. Due to this storage signal 40A, addition circuits 1 and 2 comprising the first addition means store the addition results of the addition circuit at that time, and generate storage data 1B and 2B as addition results of the first addition means. These storage data 1B and 2B are output from storage data output terminal 60.
Next, a storage signal 41A in synchronization with the next clock signal 30A is input from storage signal terminal 41. Due to this storage signal, addition circuit 3, which is the second addition means, stores the addition results within the addition circuit at that time, and generates storage data 3B as the addition result of the second addition means. These storage data 3B are output from the storage data output terminal 61.
Furthermore, a storage signal 42A synchronized with the next clock signal 30A is input from the storage signal terminal 42. Due to this storage signal 42A, counter circuit 4 stores the count value for that time and generates storage data 4A as the count result of the counter. These storage data 4A are output from storage data output terminal 62. In order to initialize the parallel counter circuit of this embodiment, a reset signal 50A is input to reset terminal 50, thereby initializing addition circuits 13 and counter circuit 4.
Next, the actions of the parallel data cementer circuit of the present embodiment will be explained with reference to the time chart shown in FIG. 3. FIG. 3 shows a series of waveform diagrams, in which (a) indicates a reset signal 50A, (b) indicates a clock signal 30A, (c) indicates parallel data 20A, (d) indicates parallel data 21A, (e) :indicates parallel data 22A, (f) indicates parallel data 23A, (g) indicates carry signal 1A of addition circuit 1, (h) indicates carry signal 2A of addition circuit 2, (i) indicates carry signal 3A of addition circuit 3, (j) indicates storage signal 40A, (k) indicates storage signal 41A, (1) indicates storage signal 42A, (m) indicates storage data 1B which is the addition result of addition circuit 1, (n) indicates a storage data 2B which is the addition result of addition circuit 2, (o) indicates storage data 3B which is the addition result of addition circuit 3 and (p) indicates storage data 4A which is the count value of counter circuit 4.
As shown in FIG. 3, the counter circuit is first initialized by the reset signal 50A at time T0. Next, at time T1, the clock signal 30A and the four parallel data 20A21A 22A and 23A are input and their calculation s begun.
Here it will be assumed that the parallel data 20A23A input at some time T2 are the data "A", "B", "C"and "D" respectively. In this case, addition circuit 1 adds "A"and "B" to generate "E" as the carry signal 1A, and addition circuit 2 adds "C" and "D" to generate "F" as the carry signal 2A, both carry signals synchronized with the clock at time T3. Then, addition circuit 3 receives the carry signals 1A and 2A, adds "E" and "F", and generates "G" as the carry signal 3A synchronized with the clock at time T4. Counter circuit 4 then receives "G" as the carry signal 3A and performs a count with the clock at time T5.
Additionally, the addition result of the input data "A", "B", "C" and "D" is retimed by a clock, as shown in the example of an addition circuit in FIG. 2. Therefore, when the storage signal 40A is entered at time T3, addition circuit 1 stores the addition result "H" of "A" and "B", and addition circuit 2 stores the addition result "I" of "C" and "D". Then, when the storage signal 41A is entered a, time T4, addition circuit 3 stores the addition result "J" of "E" and "F". Next, when the storage signal 42A is entered at time, T5, counter circuit 4 stores the result "K" of the count of "G" which is the carry signal 3A.
In this way, by inputting the storage signals 40A42A, the contents of the counter calculated from the data "A", "B", "C" and "D" at time T2 are stored.
Next, an embodiment of the parallel data counter circuit of the present invention for the case in which the parallel number is not a power of 2 will be explained with reference to FIG. 4. FIG. 4 shows an example of a triple parallel data counter circuit for counting the number of "1"s in triple parallel data.
FIG. 4 shows a first addition means comprising addition circuits 1 and 5, second addition means comprising addition circuit 3 and counter means comprising mbit counter circuit 4. Reference numerals 2022 indicate three parallel data terminals, reference numeral 30 indicates a clock terminal, reference numerals 4042 indicate storage signal terminals, reference numeral 50 indicates a reset terminal and reference numerals 6062 indicate storage data output terminals. Since addition circuit 1, addition circuit 3 and mbit counter circuit 4 are identical to those shown in FIG. 1, their explanation will be omitted.
Addition circuit 5 is a 1bit addition circuit which is necessary when the parallel number or the carry number is not a multiple of two. The addition circuit 5 performs additions with input parallel data 22. Additionally, this addition is performed so as to serially generate a carry signal 5A when there are two 1's in the parallel data 22.
Next, the composition of addition circuit 5 will be explained with reference to FIG. 5. In FIG. 5, the addition device comprises a half adder 300, DFFs 301/302 with resets, and a storage circuit 303. Reference numeral 320 indicates a data input terminal, reference numeral 330 indicates a clock terminal, reference numeral 340 indicates a storage signal terminal, reference numeral 350 indicates a reset terminal, reference numeral 370 indicates a carry output terminal and reference numeral 360 indicates a storage data output terminal.
With the addition circuit of FIG. 5, the data 320A input to data input terminal 320 and the addition result 302A of the previous step are input to half adder 300. Half adder 300 adds data 320A and addition result 302A. Then, if the addition result is greater than or equal to 2, then a carry signal 300A which is a signal to move up a place is output. The carry signal 300A is input to DFF 301. DFF 301 retimes the carry signal 300A with a clock signal 330A input to clock terminal 300, and outputs carry data 301A. These carry data are output from carry output terminal 370.
Additionally, half adder 300 outputs 300B if the addition result is either 1 or 3. The addition result 300B is retimed with the clock signal 330A at DFF 302i. The addition result 302A retimed by DFF 302 is input to half adder 300 for adding with the next data series signal 320A as the addition result of the previous step.
Additionally, the addition signal 302A is also input to storage circuit 303. Storage circuit 303 stores the current addition result 302A according to the signal 340A input to storage signal terminal 340 for reading out the calculation result for a given time, and outputs the addition signal 303A. The addition signal 303A is output from output terminal 360. DFF 301 and DFF 302 are initialized by inputting a reset signal 350A to reset terminal 350.
Next, the method by which the calculation value is calculated from the storage data in the parallel data counter circuit will be explained.
In the case of the parallel data counter circuit of FIG. 1, addition circuit 1 and addition circuit 2 independently perform calculations, while in the parallel data counter circuit of FIG. 4, addition circuit 1 and addition circuit 5 independently perform calculations. For this reason it is necessary to calculate storage data 1B and 2B for the parallel data counter circuit of FIG. 1 and storage data 1B and 5B for the parallel data counter circuit of FIG. 4. Then, assuming the value calculated by the first addition means to be x1, x1=1B+2B for the parallel data counter circuit of FIG. 1 and x1=1B+5B for the parallel data counter circuit of FIG. 4.
Additionally, addition circuit 3 comprising the second addition means adds the carry signals of addition circuit 1 and addition circuit 2 of the first addition means for the parallel data counter circuit of FIG. 1, and adds the carry signals of addition circuit 1 and addition circuit 5 for the parallel data counter circuit of FIG. 4. Carry signals 1A and 2A of addition circuit 1 comprising the first addition means in FIG. 1 and carry signals 1A and 5A of addition circuit 1 in FIG. 4 are generated when the addition result of the parallel data is 2. For this reason, the storage data 3B of addition circuit 3 comprising the second addition means has the value of "2". Assuming the value calculated by the second addition means to be x2, then x2=2* 3B.
Counter circuit 4 counts according to a carry signal 3A from addition circuit 3 comprising the second addition means. The carry signal 3A of addition circuit 3 comprising the second addition means is generated when the addition result of the carry signals 1A and 5A of addition circuits 1 and 5 comprising the first addition means is "2". This occurs when the addition result of counter circuit 4 is "4". Therefore, counter circuit 4 performs a count whenever the addition result is 4, and the storage data 4A of counter circuit 4 has the value "4". Assuming the value calculated by counter circuit 4 is x3, then x3=4* 4A. Thus, the total calculation value is their sum, so the total calculation value =x1+x2+x3. In an nparallel data counter comprising k steps of addition circuits, when assuming the result of the first addition means to be "a" the result of the second addition means to be "b", the result of the third addition means to be "c" and the value of the last counter to be "y", then the total calculation value =2^{0} *Σa+2^{1} *Σb+2^{2} *Σc . . . +2^{k} * y.
In order to calculate the Size of the circuit, the size of a circuit corresponding to a single DFF is taken as one unit. Then, taking full adder 100 of FIG. 2 to be 2 units, DFFs 101 and 102 to be 1 unit each and storage circuit 103 to be 1 unit, each addition circuit 13 in FIG. 1 has 5 units.
Additionally, taking half adder 300 of the 1bit addition circuit of FIG. 5 to be 2 units, DFFs 301302 to be 1 unit each and storage circuit 303 to be 1 unit, addition circuit 5 of FIG. 4 has 5 units.
Then, assuming mbit counter 200 and mbit storage circuit 201 comprising the mbit counter circuit in FIG. 7 each have m units, mbit counter circuit 4 of FIG. 1 and mbit counter circuits 58 of FIG. 7 are each composed of 2 * m units. Therefore, in the parallel data counter circuit of the conventional example, n*2*m units of circuit are required
On the other hand, in the parallel data counter circuit according to the present invention, if there are n pieces of parallel data, the number of circuits necessary for the first addition means would be n/2 of the addition circuits of FIG. 2 when n is an even number, and (n1)/2 of the addition circuits in FIG. 2 and one of the 1bit addition circuits in FIG. 5 when n is an odd number Additionally if the number of addition circuits composing the first addition means is n_{1}, then the second addition means requires n_{1/} 2of the addition circuits of FIG. 2 if n_{1} is an even number, and (n_{1} 1)/2 of the addition circuits of FIG. 2 and one of the 1bit addition circuits of FIG. 5 if n_{1} is odd.
In this way, if the number of addition circuits for the (K1)th addition means is n_{K1}, then n_{K1} /2 of circuits of FIG. 2 are required if n_{K1} is an even number, and (n_{K1} 1)/2 of the addition circuits of FIG. 2 and one of the 1bit addition circuits of FIG. 5 are required if n_{K1} is an odd number.
In this case, both the addition circuit of FIG. 2 and the 1bit addition circuit of FIG. 5 have 5 units of circuitry. An mbit counter circuit is necessary in addition to the abovementioned addition circuit. Therefore, in the counter circuit for n pieces of parallel data arranged according to the present invention, the amount of circuitry required is equal to (the total number of addition circuits)*5+2*m units of circuitry.
For example, when quadruple parallel data are calculated by 8bit counters, the conventional parallel data counter circuit would require 4*2*8=64 units of circuitry. In contrast, the parallel data counter circuit of the present invention is able to be put into practice with only (4/2+2/2)*5+2*8=31 units of circuitry.
Furthermore, when the count number is increased from 8 bits to 9 bits, while the conventional example requires an increase of 4*2*964=8 units of circuitry, the present invention requires only ((4/2+2/2)*5+2*9)31=2 additional units of circuitry.
Next, an example of the calculation of the size of a parallel data counter circuit when quintuple parallel data are calculated by 8bit counters will be explained. In this case, the conventional example would have 5*2*8=80 units of circuitry. However, according to the present invention, only ((51)/2+1+(31)/2+1+2/2)*5+2*8=46 units of circuitry are required.
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Cited By (2)
Publication number  Priority date  Publication date  Assignee  Title 

US5999961A (en) *  19970915  19991207  California Institute Of Technology  Parallel prefix operations in asynchronous processors 
US6747471B1 (en)  20020110  20040608  Taiwan Semiconductor Manufacturing Company  Method and apparatus to estimate burnin time by measurement of scribeline devices, with stacking devices, and with common pads 
Citations (5)
Publication number  Priority date  Publication date  Assignee  Title 

US3711692A (en) *  19710315  19730116  Goodyear Aerospace Corp  Determination of number of ones in a data field by addition 
US4189716A (en) *  19770324  19800219  Bell Telephone Laboratories, Incorporated  Circuit for determining the number of ones in a binary signal 
US4206505A (en) *  19780525  19800603  Kazmin Evgeny V  Random process initial moments computer 
US4488253A (en) *  19810508  19841211  Itt Industries, Inc.  Parallel counter and application to binary adders 
US4669089A (en) *  19850930  19870526  The Boeing Company  Suppressed clock pulseduration modulator for direct sequence spread spectrum transmission systems 
Patent Citations (5)
Publication number  Priority date  Publication date  Assignee  Title 

US3711692A (en) *  19710315  19730116  Goodyear Aerospace Corp  Determination of number of ones in a data field by addition 
US4189716A (en) *  19770324  19800219  Bell Telephone Laboratories, Incorporated  Circuit for determining the number of ones in a binary signal 
US4206505A (en) *  19780525  19800603  Kazmin Evgeny V  Random process initial moments computer 
US4488253A (en) *  19810508  19841211  Itt Industries, Inc.  Parallel counter and application to binary adders 
US4669089A (en) *  19850930  19870526  The Boeing Company  Suppressed clock pulseduration modulator for direct sequence spread spectrum transmission systems 
Cited By (2)
Publication number  Priority date  Publication date  Assignee  Title 

US5999961A (en) *  19970915  19991207  California Institute Of Technology  Parallel prefix operations in asynchronous processors 
US6747471B1 (en)  20020110  20040608  Taiwan Semiconductor Manufacturing Company  Method and apparatus to estimate burnin time by measurement of scribeline devices, with stacking devices, and with common pads 
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